Unluckily, it is not possible to increase the boot volume storage on a running Amazon EC2 instance.
But this can be done with a minimal downtime without needing to start a new instance.
To have it done with minimal downtime, I would recommend you to test it with a throwaway EC2 instance so that you get acquainted to the procedure and later do it with just a few minutes downtime for the actual EC2 instance.
Keep Learning :)